For centuries, the primary technical meaning of image has been a visual representation or counterpart, formed through the interaction of light with mirrors and lenses, and recorded through a photochemical process. In digital photography, the photochemical process has been replaced by a sensor array, but the use of optical elements is unchanged. Thus, the spatial resolution in this traditional imaging is limited by the quality of the optics and the number of sensors in the array. This project develops the foundations of achieving spatial resolution, in 2D and 3D, by measuring temporal variations of light intensity in response to temporally- or spatiotemporally-varying illumination. This is a radical departure from traditional imaging, in which time is associated only with fixing the period over which light must be collected to achieve the desired contrast. Reducing requirements for lenses, mirrors, and numbers of sensors can both lower costs and enable entirely new imaging configurations. Of particular interest is to enable 3D capture in mobile devices such as cell phones.
Space-from-time imaging (SFTI) is based on the recognition that information of interest in a scene, such as bidirectional reflectance distribution functions at various wavelengths and distances from the imaging device, are embedded in the transfer function from a light source to a light sensor. Furthermore, light transfer is linear. Thus, SFTI introduces new inverse problems with at least portions of the forward models being linear. The investigators will apply and extend analysis techniques developed for other imaging methods, such as computed tomography and synthetic aperture radar, to develop theoretical foundations for SFTI. Analysis will inspire and be informed by proof-of-concept experiments.
